Finite Group Databasebeta

← #27084839

Subgroups — #27084839

Order 12032.

2152 conjugacy classes of subgroups.

The subgroup lattice has 1212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256804C211yesmaximal, characteristic, complemented
2C4×#13094069C211yesmaximal, characteristic, complemented
3#20253654C212yesmaximal, complemented
4#20253630C212yesmaximal, complemented
5#20253591C212yesmaximal, complemented
6#20253576C212yesmaximal, complemented
7#20253444C212yesmaximal, complemented
8#20253439C212yesmaximal, complemented
9#20253410C212yesmaximal, complemented
10#20253386C212yesmaximal, complemented
11#20253365C211yesmaximal, characteristic, complemented
12#20253348C211yesmaximal, characteristic, complemented
13#20253238C211yesmaximal, characteristic, complemented
14#20253221C211yesmaximal, characteristic, complemented
15#20252926C211yesmaximal, characteristic, complemented
16#20252893C211yesmaximal, characteristic, complemented
17#20252691C211yesmaximal, characteristic, complemented
18#20252657C211yesmaximal, characteristic, complemented
19C4×#13094052C211yesmaximal, characteristic, complemented
20C4×#13094044C211yesmaximal, characteristic, complemented
21C2×C4×#10625334C211yesmaximal, characteristic, complemented
22#20252033C211yesmaximal, characteristic, complemented
23C4×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
24C2×#13094069C2211yescharacteristic
25C2×#13094052C2211yescharacteristic
26C2×#13094044C2211yescharacteristic
27C22×#10625334C2211yescharacteristic
28#15689751C2211yescharacteristic, complemented
29#15689745C2212yescomplemented
30#15689744—21no—
31#15689728—21no—
32#15689724C2212yescomplemented
33#15689706—22no—
34#15689701C2211yescharacteristic
35#15689692C2211yescharacteristic
36#15689687C2211yescharacteristic, complemented
37#15689673—21no—
38#15689670C2212yescomplemented
39#15689660C2212yescomplemented
40#15689657—21no—
41#15689632—22no—
42#15689604C2211yescharacteristic
43#15689604C2211yescharacteristic
44#15689602—21no—
45#15689602C2212yescomplemented
46#15689598C2211yescharacteristic
47#15689596—22no—
48#15689595—21no—
49#15689595C2212yescomplemented
50C4×#10625350C2211yescharacteristic
51C4×#10625350C2211yescharacteristic
52C4×#10625352—21no—
53C4×#10625352C2212yescomplemented
54C2×C4×D188C2211yescharacteristic, complemented
55C2×C4×C22⋊D47—22no—
56C4×D4×D47—21no—
57C4×D4×D47C2212yescomplemented
58#15689462C2212yescomplemented
59#15689457C2212yescomplemented
60#15689450C2212yescomplemented
61#15689449C2212yescomplemented
62#15689446C2212yescomplemented
63#15689443C2212yescomplemented
64#15689438C2212yescomplemented
65#15689435C2212yescomplemented
66#15689433C2212yescomplemented
67#15689425C2212yescomplemented
68#15689422C2212yescomplemented
69#15689421C2212yescomplemented
70#15689417C2212yescomplemented
71#15689411C2212yescomplemented
72#15689402C2212yescomplemented
73#15689401C2212yescomplemented
74#15689348C2212yescomplemented
75#15689341C2212yescomplemented
76#15689340C2212yescomplemented
77#15689340C2212yescomplemented
78#15689322C2212yescomplemented
79#15689317C2212yescomplemented
80#15689316C2212yescomplemented
81#15689316C2212yescomplemented
82#15689282C2212yescomplemented
83#15689272C2212yescomplemented
84#15689269C2212yes—
85#15689269C2212yes—
86#15689265C2212yescomplemented
87#15689258C2212yes—
88#15689258C2212yes—
89#15689255C2212yescomplemented
90#15689236C2212yescomplemented
91#15689225C2212yescomplemented
92C4×#10625337C2211yescharacteristic, complemented
93C4×#10625337C2211yescharacteristic, complemented
94C4×#10625325C2212yescomplemented
95C4×#10625336C2211yescharacteristic, complemented
96C4×#10625336C2211yescharacteristic, complemented
97C4×#10625335C2211yescharacteristic, complemented
98C4×#10625335C2211yescharacteristic, complemented
99C4×D376C2212yescomplemented
100C4×#10625334C2212yescomplemented
101C4×#10625334C2212yescomplemented
102C4×#10625334C2211yescharacteristic, complemented
103C4×#10625334C2212yescomplemented
104C4×#10625334C2211yescharacteristic, complemented
105C4×#10625334C2212yescomplemented
106#15689185C2212yescomplemented
107#15689185C2212yescomplemented
108#15689174C2212yescomplemented
109#15689174C2212yescomplemented
110#15689165C2211yescharacteristic, complemented
111#15689159C2211yescharacteristic, complemented
112C2×#13093957C2211yescharacteristic, complemented
113#15689151C2211yescharacteristic, complemented
114#15689151C2211yescharacteristic, complemented
115#15689129C2211yescharacteristic, complemented
116#15689125C2211yescharacteristic
117#15689119C2211yescharacteristic, complemented
118#15689117C2211yescharacteristic
119C2×#13093945C2211yescharacteristic
120C2×#13093944C2211yescharacteristic, complemented
121#15689091C2211yescharacteristic
122#15689091C2211yescharacteristic
123C2×C4×C47⋊C8C2211yescharacteristic, complemented
124C2×AGL(1,ℤ/8)×C47C2211yescharacteristic
125C4×#41×C47C2211yescharacteristic, complemented
126C2×C4×D4×C47C2211yescharacteristic
127C47×#442C2212yescomplemented
128C47×#440C2212yescomplemented
129C4×SD16×C47C2212yescomplemented
130C4×D8×C47C2212yescomplemented
131C47×#428C2211yescharacteristic, complemented
132C47×#418C2211yescharacteristic
133C47×#417C2211yescharacteristic, complemented
134C4×M16×C47C2211yescharacteristic, complemented
135#13094069—24no—
136#13094069—24no—
137C2×#10625350—22no—
138C2×#10625350C2311yescharacteristic
139C2×#10625350C2311yescharacteristic
140C2×#10625352—21no—
141C2×#10625352C2312yes—
142C22×D188C2311yescharacteristic
143C22×C22⋊D47—22no—
144C2×D4×D47—21no—
145C2×D4×D47C2312yes—
146C22×C4×D47—21no—
147C22×C4×D47—22no—
148#13094052—24no—
149#13094044—24no—
150C2×#10625337C2311yescharacteristic
151C2×#10625325C2312yes—
152C2×#10625335C2311yescharacteristic
153C2×#10625336C2311yescharacteristic
154C2×D376C2312yes—
155C2×#10625334—24no—
156C2×#10625334C2311yescharacteristic
157C2×#10625334C2312yes—
158C2×#10625334C2312yes—
159C22×C47⋊C8C2311yescharacteristic
160C22×C47⋊C8C2311yescharacteristic
161#13094024—21no—
162#13094023C2312yes—
163#13094021—21no—
164#13094020C2312yes—
165#13094019—22no—
166#13094018—22no—
167#13094016—21no—
168#13094015C2312yes—
169#13094013C2312yes—
170#13094012—21no—
171#13094012—22no—
172#13094010—22no—
173#13094009—22no—
174#13094009—22no—
175#13094007—22no—
176#13094006—22no—
177#13094003—21no—
178#13094002—22no—
179#13094001—22no—
180#13094000C2312yes—
181#13093999C2312yes—
182#13093999C2312yes—
183#13093998—21no—
184#13093998—22no—
185#13093998—21no—
186#13093998—21no—
187#13093997—22no—
188#13093997—22no—
189#13093996—22no—
190#13093995C2312yes—
191#13093994—22no—
192#13093992—22no—
193C4×Dic94D411yescharacteristic
194C4×Dic94D411yescharacteristic
195C4×Dic94C2311yescharacteristic
196C4×Dic94C2311yescharacteristic
197#13093989—21no—
198#13093989C2312yes—
199C4×D188—22no—
200C4×D188—21no—
201C4×D188—21no—
202C4×D188D411yescharacteristic
203C4×D188D411yescharacteristic
204C4×D188C2312yes—
205C4×D188C2311yescharacteristic
206C4×D188C2311yescharacteristic
207C4×D188C2312yes—
208D4×Dic47—21no—
209D4×Dic47—21no—
210D4×Dic47C2312yes—
211D4×Dic47C2312yes—
212#13093986—21no—
213#13093986C2312yes—
214C4×C22⋊D47—21no—
215C4×C22⋊D47—21no—
216C4×C22⋊D47—22no—
217C4×C22⋊D47—22no—
218C4×C22⋊D47—22no—
219C4×C22⋊D47—22no—
220C4×C22⋊D47—22no—
221C4×C22⋊D47—22no—
222C4×C22⋊D47—22no—
223C4×C22⋊D47D412yes—
224C4×C22⋊D47D412yes—
225(C22⋊D47)⋊C4—22no—
226(C22⋊D47)⋊C4—22no—
227(C22⋊D47)⋊C4—22no—
228(C22⋊D47)⋊C4—22no—
229#13093983C2311yescharacteristic
230#13093983C2311yescharacteristic
231#13093982—21no—
232#13093982C2312yes—
233#13093981—21no—
234#13093981—22no—
235#13093981C2312yes—
236#13093980—22no—
237#13093980—22no—
238C2×C4⋊Dic47C2311yescharacteristic
239C2×Dic47⋊C4—22no—
240C4⋊C4×D47—21no—
241C4⋊C4×D47C2312yes—
242C2×C22⋊Dic47—22no—
243C2×(C2×D47)⋊C4—21no—
244C2×(C2×D47)⋊C4—22no—
245C22⋊C4×D47—22no—
246C22⋊C4×D47—22no—
247C2×C4×Dic47—22no—
248C42×D47—21no—
249C42×D47C2312yes—
250#13093958C2312yes—
251#13093957C2311yescharacteristic
252#13093957C2311yescharacteristic
253#13093957C2312yes—
254#13093957C2312yes—
255#13093956C2312yes—
256#13093955C2311yescharacteristic
257#13093955C2311yescharacteristic
258Dic47⋊C8C2312yes—
259Dic47⋊C8C2312yes—
260Dic47⋊C8C2312yes—
261Dic47⋊C8C2312yes—
262#13093949C2312yes—
263#13093948C2311yescharacteristic
264#13093948C2311yescharacteristic
265#13093947C2311yescharacteristic
266#13093947C2311yescharacteristic
267#13093946C2312yes—
268#13093946C2312yes—
269#13093946C2312yes—
270#13093945C2312yes—
271#13093945C2312yes—
272#13093945C2311yescharacteristic
273#13093945C2311yescharacteristic
274#13093944C2311yescharacteristic
275#13093944C2311yescharacteristic
276#13093944C2312yes—
277#13093944C2312yes—
278(C2×D47)⋊C8C2312yes—
279(C2×D47)⋊C8C2312yes—
280(C2×D47)⋊C8C2312yes—
281(C2×D47)⋊C8C2312yes—
282C4×C47⋊C8C2311yescharacteristic
283C4×C47⋊C8C2311yescharacteristic
284C4×C47⋊C8C2311yescharacteristic
285C4×C47⋊C8C2311yescharacteristic
286C2×#41×C47C2311yescharacteristic
287C22×D4×C47C2311yescharacteristic
288C23×C4×C47—21no—
289AGL(1,ℤ/8)×C47—24no—
290C2×SD16×C47C2312yes—
291C2×D8×C47C2312yes—
292C2×M16×C47C2311yescharacteristic
293C2×M16×C47C2311yescharacteristic
294C4×Q8×C47C2311yescharacteristic
295C4×Q8×C47C2311yescharacteristic
296C4×D4×C47—21no—
297C4×D4×C47—21no—
298C4×D4×C47—21no—
299C4×D4×C47—21no—
300C4×D4×C47C2312yes—
301C4×D4×C47C2312yes—
302C4×D4×C47C2311yescharacteristic
303C4×D4×C47C2311yescharacteristic
304#117×C47—21no—
305#117×C47C2311yescharacteristic
306C2×C4⋊C4×C47C2311yescharacteristic
307C2×C22⋊C4×C47—21no—
308C2×C42×C47—21no—
309C2×C42×C47C2311yescharacteristic
310#107×C47C2312yes—
311#106×C47C2312yes—
312#103×C47C2312yes—
313#102×C47C2312yes—
314#102×C47C2312yes—
315#102×C47C2312yes—
316#97×C47C2312yes—
317C4×C8×C47C2312yes—
318C24×C47—21no—
319C23×D47—22no—
320C23×D47—21no—
321#41×C47—22no—
322#41×C47—22no—
323C2×Q8×C47C2411yescharacteristic
324C2×D4×C47—21no—
325C2×D4×C47—21no—
326C2×D4×C47—22no—
327C2×D4×C47#4114yescomplemented
328C2×D4×C47C2411yescharacteristic
329C2×D4×C47C2412yes—
330C22×C4×C47—21no—
331C22×C4×C47—21no—
332C22×C4×C47—21no—
333C22×C4×C47—22no—
334C22×C4×C47—21no—
335C22×C4×C47—22no—
336C22×C4×C47—82no—
337C22×C4×C47C2×D411yescharacteristic
338C22×C4×C47C2×D411yescharacteristic
339C22×C4×C47C2411yescharacteristic
340C2×C22⋊D47—216no—
341C2×C22⋊D47—21no—
342C2×C22⋊D47—22no—
343C2×C22⋊D47—22no—
344C2×C22⋊D47—22no—
345C2×C22⋊D47—22no—
346C2×C22⋊D47—22no—
347C2×C22⋊D47C2×D412yes—
348C22×Dic47—22no—
349C22×Dic47—21no—
350C22×Dic47—22no—
351C22×Dic47—22no—
352#10625352—28no—
353#10625352—24no—
354#10625352—24no—
355D4×D47—28no—
356D4×D47—24no—
357D4×D47—24no—
358#10625350—22no—
359#10625350—22no—
360#10625350—22no—
361#10625350—84no—
362#10625350#4114yescomplemented
363C2×D188—22no—
364C2×D188—22no—
365C2×D188—21no—
366C2×D188—22no—
367C2×D188—22no—
368C2×D188C2×D411yescharacteristic
369C2×D188C2412yes—
370C2×D188C2411yescharacteristic
371C2×C4×D47—21no—
372C2×C4×D47—21no—
373C2×C4×D47—22no—
374C2×C4×D47—22no—
375C2×C4×D47—21no—
376C2×C4×D47—22no—
377C2×C4×D47—22no—
378C2×C4×D47—84no—
379C2×C4×D47—82no—
380C2×C4×D47C2×D412yes—
381C2×C4×D47C2×D412yes—
382C2×C4×D47C2412yes—
383C2×Dic94—22no—
384C2×Dic94C2×D411yescharacteristic
385C2×Dic94C2411yescharacteristic
386SD16×C47—24no—
387D8×C47—24no—
388M16×C47—22no—
389M16×C47—22no—
390C2×C8×C47C2412yes—
391C2×C8×C47C2412yes—
392C4⋊C4×C47—21no—
393C4⋊C4×C47—21no—
394C4⋊C4×C47—21no—
395C4⋊C4×C47C2412yes—
396C4⋊C4×C47C2411yescharacteristic
397C4⋊C4×C47C2411yescharacteristic
398C22⋊C4×C47—21no—
399C22⋊C4×C47—22no—
400C22⋊C4×C47—22no—
401C22⋊C4×C47—21no—
402C22⋊C4×C47—21no—
403C42×C47—21no—
404C42×C47—21no—
405C42×C47—21no—
406C42×C47C2×D411yescharacteristic
407C42×C47C2×D411yescharacteristic
408C42×C47C2411yescharacteristic
409C42×C47C2411yescharacteristic
410C22⋊Dic47—21no—
411C22⋊Dic47—22no—
412C22⋊Dic47—22no—
413C22⋊Dic47—22no—
414C22⋊Dic47C2×D412yes—
415#10625337—22no—
416#10625336—22no—
417#10625335—22no—
418#10625334—24no—
419#10625334—24no—
420#10625334—22no—
421(C2×D47)⋊C4—22no—
422(C2×D47)⋊C4—22no—
423(C2×D47)⋊C4—21no—
424(C2×D47)⋊C4—21no—
425(C2×D47)⋊C4—22no—
426(C2×D47)⋊C4—22no—
427(C2×D47)⋊C4—22no—
428(C2×D47)⋊C4—22no—
429(C2×D47)⋊C4—22no—
430(C2×D47)⋊C4—22no—
431(C2×D47)⋊C4—22no—
432(C2×D47)⋊C4C2×D412yes—
433(C2×D47)⋊C4C2×D412yes—
434C4⋊Dic47—21no—
435C4⋊Dic47—22no—
436C4⋊Dic47C2×D411yescharacteristic
437C4⋊Dic47C2×D411yescharacteristic
438C4⋊Dic47C2412yes—
439C4⋊Dic47C2411yescharacteristic
440C4⋊Dic47C2411yescharacteristic
441Dic47⋊C4—21no—
442Dic47⋊C4—21no—
443Dic47⋊C4—22no—
444Dic47⋊C4—22no—
445Dic47⋊C4—22no—
446Dic47⋊C4—22no—
447Dic47⋊C4—22no—
448Dic47⋊C4C2×D412yes—
449Dic47⋊C4C2×D412yes—
450C4×Dic47—21no—
451C4×Dic47—21no—
452C4×Dic47—21no—
453C4×Dic47—22no—
454C4×Dic47—22no—
455C4×Dic47C2×D412yes—
456C4×Dic47C2×D412yes—
457C4×Dic47C2412yes—
458C2×C47⋊C8—22no—
459C2×C47⋊C8—22no—
460C2×C47⋊C8C2411yescharacteristic
461C2×C47⋊C8C2411yescharacteristic
462C2×C47⋊C8C2411yescharacteristic
463C2×C47⋊C8C2411yescharacteristic
464D376—24no—
465#10625325—24no—
466C23×C47—22no—
467C23×C47—24no—
468C23×C47—21no—
469C23×C47—81no—
470C23×C47—81no—
471C23×C47C22×D411yescharacteristic
472C22×D47—21no—
473C22×D47—28no—
474C22×D47—22no—
475C22×D47—42no—
476C22×D47—82no—
477C22×D47—82no—
478C22×D47—81no—
479C22×D47—81no—
480C22×D47C22×D412yes—
481Q8×C47—21no—
482Q8×C47—21no—
483D4×C47—24no—
484D4×C47—22no—
485D4×C47—21no—
486D4×C47—21no—
487D4×C47—42no—
488D4×C47C2×#4114yes—
489C2×C4×C47—22no—
490C2×C4×C47—22no—
491C2×C4×C47—21no—
492C2×C4×C47—21no—
493C2×C4×C47—21no—
494C2×C4×C47—41no—
495C2×C4×C47—42no—
496C2×C4×C47—44no—
497C2×C4×C47—42no—
498C2×C4×C47—81no—
499C2×C4×C47—82no—
500C2×C4×C47—81no—
501C2×C4×C47C22×D411yescharacteristic
502C2×C4×C47C22×D411yescharacteristic
503C2×C4×C47C22×D411yescharacteristic
504C2×C4×C47C22×D411yescharacteristic
505C2×C4×C47C22×D411yescharacteristic
506C2×C4×C47C2×#4112yes—
507C2×C4×C47C2×#4112yes—
508C2×C4×C47C2511yescharacteristic
509C22⋊D47—28no—
510C22⋊D47—28no—
511C22⋊D47—24no—
512C22⋊D47—24no—
513C22⋊D47—82no—
514C22⋊D47—82no—
515C22⋊D47—82no—
516C2×Dic47—28no—
517C2×Dic47—21no—
518C2×Dic47—21no—
519C2×Dic47—21no—
520C2×Dic47—22no—
521C2×Dic47—82no—
522C2×Dic47—82no—
523C2×Dic47—81no—
524C2×Dic47C22×D412yes—
525C2×Dic47C22×D412yes—
526C2×Dic47C22×D412yes—
527D188—22no—
528D188—21no—
529D188—22no—
530D188—22no—
531D188—42no—
532D188—82no—
533D188—82no—
534D188C2×#4112yes—
535C4×D47—24no—
536C4×D47—24no—
537C4×D47—22no—
538C4×D47—22no—
539C4×D47—42no—
540C4×D47—42no—
541C4×D47—44no—
542C4×D47—82no—
543C4×D47—81no—
544C4×D47—82no—
545C4×D47—82no—
546Dic94—22no—
547Dic94—21no—
548Dic94—82no—
549Dic94C2×#4112yes—
550C8×C47—22no—
551C8×C47—22no—
552C47⋊C8—21no—
553C47⋊C8—21no—
554C47⋊C8—21no—
555C47⋊C8—21no—
556#60570—471nomaximal, Sylow
557C22×C47—21no—
558C22×C47—21no—
559C22×C47—24no—
560C22×C47—42no—
561C22×C47—42no—
562C22×C47—41no—
563C22×C47—41no—
564C22×C47—41no—
565C22×C47—84no—
566C22×C47#52512yes—
567C22×C47C23×D411yescharacteristic
568C2×D47—22no—
569C2×D47—22no—
570C2×D47—22no—
571C2×D47—22no—
572C2×D47—41no—
573C2×D47—41no—
574C2×D47—42no—
575C2×D47—42no—
576C2×D47—42no—
577C2×D47—88no—
578C2×D47—84no—
579C4×C47—21no—
580C4×C47—21no—
581C4×C47—21no—
582C4×C47—41no—
583C4×C47—41no—
584C4×C47—41no—
585C4×C47—42no—
586C4×C47#52512yes—
587C4×C47#57612yes—
588C4×C47C22×#4111yescharacteristic
589C4×C47C22×#4111yescharacteristic
590Dic47—22no—
591Dic47—22no—
592Dic47—22no—
593Dic47—22no—
594Dic47—41no—
595Dic47—42no—
596Dic47—41no—
597#3460—471no—
598C4×H(5,𝔽2)—471no—
599#3124—472no—
600#3122—472no—
601#3119—472no—
602#3118—472no—
603#3106—472no—
604#3105—472no—
605#3102—472no—
606#3100—472no—
607#3098—471no—
608#3096—471no—
609#3083—471no—
610#3081—471no—
611#3045—471no—
612#3041—471no—
613#3012—471no—
614#3008—471no—
615C4×AGL(1,ℤ/8)—471no—
616C4×AGL(1,ℤ/8)D4711yescharacteristic, complemented
617C4×#135—471no—
618C2×C4×D8—471no—
619#2922—471no—
620C2×C47—22no—
621C2×C47—44no—
622C2×C47—81no—
623C2×C47C2×#52511yescharacteristic
624C2×C47C2×#57611yescharacteristic
625C2×C47#358411yescharacteristic
626D47—42no—
627D47—42no—
628D47—82no—
629C2×H(5,𝔽2)—471no—
630C2×AGL(1,ℤ/8)—471no—
631C2×AGL(1,ℤ/8)C2×D4711yescharacteristic
632C2×#135—471no—
633C22×D8—471no—
634#544—471no—
635#542—472no—
636#542—941no—
637#540—472no—
638#540—941no—
639#538—942no—
640#537—471no—
641#535—471no—
642#535—471no—
643#532—472no—
644#532—941no—
645#529—472no—
646#529—941no—
647#525—942no—
648#520—471no—
649#520—472no—
650#520—471no—
651#520—941no—
652#518—471no—
653#518—472no—
654#518—942no—
655#518—941no—
656C4×#41—471no—
657C4×#41—472no—
658C4×#41—471no—
659C4×#41—941no—
660C4×#41C2×D4711yescharacteristic, complemented
661C2×C4×D4—472no—
662C2×C4×D4—471no—
663C2×C4×D4—941no—
664C2×C4×D4—942no—
665C2×C4×D4C2×D4711yescharacteristic
666#485—472no—
667#484—472no—
668#482—472no—
669#482—472no—
670#482—472no—
671#481—472no—
672#480—472no—
673#480—472no—
674#479—472no—
675#478—472no—
676#478—472no—
677#478—472no—
678#477—472no—
679#476—472no—
680#474—472no—
681#474—472no—
682#464—472no—
683#463—472no—
684#463—472no—
685#463—472no—
686#460—472no—
687#459—472no—
688#459—472no—
689#459—472no—
690#452—472no—
691#450—472no—
692#449—472no—
693#449—472no—
694#449—472no—
695#447—472no—
696#447—472no—
697#447—472no—
698#442—472no—
699#442C2×D4712yescomplemented
700#440—472no—
701#440C2×D4712yescomplemented
702C4×Q16—471no—
703C4×Q16—471no—
704C4×SD16—471no—
705C4×SD16—471no—
706C4×SD16—471no—
707C4×SD16—471no—
708C4×SD16—472no—
709C4×SD16C2×D4712yescomplemented
710C4×D8—471no—
711C4×D8—472no—
712C4×D8—472no—
713C4×D8—472no—
714C4×D8—471no—
715C4×D8—472no—
716C4×D8—472no—
717C4×D8C2×D4712yescomplemented
718#433—472no—
719#433—472no—
720#431—472no—
721#431—472no—
722#428—471no—
723#428C2×D4711yescharacteristic, complemented
724#427—471no—
725C2×#107—471no—
726#424—471no—
727#424—471no—
728#418—471no—
729#418C2×D4711yescharacteristic
730#417—471no—
731#417C2×D4711yescharacteristic, complemented
732#416—471no—
733#416—471no—
734C2×#102—471no—
735C2×#102—471no—
736#408—471no—
737#408—471no—
738C4×M16C2×D4711yescharacteristic, complemented
739C2×C4×C8—471no—
740C47#6057011yescharacteristic, complemented, Sylow
741H(5,𝔽2)—944no—
742H(5,𝔽2)—944no—
743C2×#41—471no—
744C2×#41—472no—
745C2×#41—471no—
746C2×#41—942no—
747C2×#41—941no—
748C2×#41C22×D4711yescharacteristic
749C22×D4—472no—
750C22×D4—471no—
751C22×D4—941no—
752C22×D4—942no—
753C22×D4C22×D4711yescharacteristic
754C23×C4—21no—
755C23×C4—942no—
756C23×C4—941no—
757AGL(1,ℤ/8)—24no—
758AGL(1,ℤ/8)—944no—
759#135—944no—
760C2×Q16—471no—
761C2×SD16—471no—
762C2×SD16—471no—
763C2×SD16—472no—
764C2×SD16C22×D4712yes—
765C2×D8—472no—
766C2×D8—472no—
767C2×D8—471no—
768C2×D8—472no—
769C2×D8—944no—
770C2×D8C22×D4712yes—
771C2×M16C22×D4711yescharacteristic
772C2×M16C22×D4711yescharacteristic
773C22×C8—471no—
774C22×C8—471no—
775C4⋊Q8—472no—
776C4⋊Q8—941no—
777#127—472no—
778#127—941no—
779#126—942no—
780#126—942no—
781#125—472no—
782#125—941no—
783#124—472no—
784#124—942no—
785#124—941no—
786#124—942no—
787#123—942no—
788#123—942no—
789#123—942no—
790#123—942no—
791C22⋊Q8—472no—
792C22⋊Q8—942no—
793C22⋊Q8—942no—
794C22⋊Q8—941no—
795#121—472no—
796#121—472no—
797#121—472no—
798#121—942no—
799#121—942no—
800#121—942no—
801#121—941no—
802#121—941no—
803#121—941no—
804#121—942no—
805#120—942no—
806#120—942no—
807C4×Q8—471no—
808C4×Q8—471no—
809C4×Q8—472no—
810C4×Q8—471no—
811C4×Q8—471no—
812C4×Q8—941no—
813C4×Q8C22×D4711yescharacteristic
814C4×Q8C22×D4711yescharacteristic
815C4×D4—21no—
816C4×D4—21no—
817C4×D4—21no—
818C4×D4—21no—
819C4×D4—472no—
820C4×D4—472no—
821C4×D4—472no—
822C4×D4—472no—
823C4×D4—472no—
824C4×D4—471no—
825C4×D4—471no—
826C4×D4—471no—
827C4×D4—472no—
828C4×D4—472no—
829C4×D4—471no—
830C4×D4—942no—
831C4×D4—942no—
832C4×D4—942no—
833C4×D4—942no—
834C4×D4—942no—
835C4×D4—942no—
836C4×D4—942no—
837C4×D4—942no—
838C4×D4—942no—
839C4×D4—941no—
840C4×D4—942no—
841C4×D4—941no—
842C4×D4—941no—
843C4×D4—942no—
844C4×D4—942no—
845C4×D4—941no—
846C4×D4—941no—
847C4×D4—941no—
848C4×D4—941no—
849C4×D4C22×D4712yes—
850C4×D4C22×D4712yes—
851C4×D4C22×D4711yescharacteristic
852C4×D4C22×D4711yescharacteristic
853#117—21no—
854#117—471no—
855#117—472no—
856#117—471no—
857#117—472no—
858#117—942no—
859#117—942no—
860#117—942no—
861#117—941no—
862#117—941no—
863#117C22×D4711yescharacteristic
864C2×C4⋊C4—471no—
865C2×C4⋊C4—472no—
866C2×C4⋊C4—941no—
867C2×C4⋊C4—942no—
868C2×C4⋊C4C22×D4711yescharacteristic
869C2×C22⋊C4—21no—
870C2×C22⋊C4—942no—
871C2×C22⋊C4—942no—
872C2×C22⋊C4—942no—
873C2×C22⋊C4—942no—
874C2×C22⋊C4—941no—
875C2×C42—21no—
876C2×C42—472no—
877C2×C42—942no—
878C2×C42—941no—
879C2×C42C22×D4711yescharacteristic
880#107—472no—
881#107—472no—
882#107—472no—
883#107—471no—
884#107—471no—
885#107C22×D4712yes—
886#106—472no—
887#106—471no—
888#106—471no—
889#106C22×D4712yes—
890C4⋊C8—472no—
891C4⋊C8—472no—
892C4⋊C8—472no—
893C4⋊C8—472no—
894#103—471no—
895#103—471no—
896#103—472no—
897#103—471no—
898#103—471no—
899#103C22×D4712yes—
900#102—472no—
901#102—472no—
902#102—471no—
903#102—471no—
904#102—472no—
905#102—472no—
906#102—472no—
907#102—472no—
908#102—472no—
909#102—471no—
910#102—471no—
911#102C22×D4712yes—
912#102C22×D4712yes—
913#102C22×D4712yes—
914C22⋊C8—472no—
915C22⋊C8—472no—
916C22⋊C8—472no—
917C22⋊C8—472no—
918#97C22×D4712yes—
919C4×C8—471no—
920C4×C8—471no—
921C4×C8—471no—
922C4×C8—471no—
923C4×C8C22×D4712yes—
924C24—21no—
925C24—942no—
926C24—941no—
927#41—22no—
928#41—22no—
929#41—474no—
930#41—944no—
931#41—948no—
932#41—944no—
933#41—942no—
934#41—942no—
935#41—942no—
936#41—3764no—
937C2×Q8—471no—
938C2×Q8—471no—
939C2×Q8—942no—
940C2×Q8C23×D4711yescharacteristic
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—22no—
944C2×D4—472no—
945C2×D4—471no—
946C2×D4—471no—
947C2×D4—472no—
948C2×D4—942no—
949C2×D4—942no—
950C2×D4—942no—
951C2×D4—942no—
952C2×D4—942no—
953C2×D4—944no—
954C2×D4—948no—
955C2×D4—942no—
956C2×D4—9416no—
957C2×D4—941no—
958C2×D4—944no—
959C2×D4—942no—
960C2×D4—941no—
961C2×D4—942no—
962C2×D4—942no—
963C2×D4#1062535014yescomplemented
964C2×D4C23×D4711yescharacteristic
965C2×D4C23×D4712yes—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—22no—
970C22×C4—21no—
971C22×C4—22no—
972C22×C4—82no—
973C22×C4—472no—
974C22×C4—472no—
975C22×C4—472no—
976C22×C4—942no—
977C22×C4—942no—
978C22×C4—942no—
979C22×C4—942no—
980C22×C4—942no—
981C22×C4—941no—
982C22×C4—941no—
983C22×C4—941no—
984C22×C4—942no—
985C22×C4—941no—
986C22×C4—942no—
987C22×C4—3762no—
988C22×C4—3764no—
989C22×C4D4×D4711yescharacteristic
990C22×C4D4×D4711yescharacteristic
991C22×C4C23×D4711yescharacteristic
992Q16—942no—
993SD16—24no—
994SD16—944no—
995SD16—942no—
996SD16—942no—
997D8—24no—
998D8—944no—
999D8—942no—
1000D8—944no—
1001D8—944no—
1002M16—22no—
1003M16—22no—
1004C2×C8—471no—
1005C2×C8—471no—
1006C2×C8—471no—
1007C2×C8—471no—
1008C2×C8—942no—
1009C2×C8—942no—
1010C2×C8C23×D4712yes—
1011C2×C8C23×D4712yes—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—472no—
1016C4⋊C4—472no—
1017C4⋊C4—471no—
1018C4⋊C4—471no—
1019C4⋊C4—471no—
1020C4⋊C4—471no—
1021C4⋊C4—472no—
1022C4⋊C4—942no—
1023C4⋊C4—942no—
1024C4⋊C4—942no—
1025C4⋊C4—942no—
1026C4⋊C4—942no—
1027C4⋊C4—942no—
1028C4⋊C4—941no—
1029C4⋊C4—941no—
1030C4⋊C4—941no—
1031C4⋊C4C23×D4712yes—
1032C4⋊C4C23×D4711yescharacteristic
1033C4⋊C4C23×D4711yescharacteristic
1034C22⋊C4—21no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—21no—
1038C22⋊C4—21no—
1039C22⋊C4—472no—
1040C22⋊C4—472no—
1041C22⋊C4—472no—
1042C22⋊C4—942no—
1043C22⋊C4—942no—
1044C22⋊C4—942no—
1045C22⋊C4—942no—
1046C22⋊C4—942no—
1047C22⋊C4—942no—
1048C22⋊C4—942no—
1049C22⋊C4—942no—
1050C22⋊C4—942no—
1051C22⋊C4—942no—
1052C22⋊C4—941no—
1053C22⋊C4—941no—
1054C22⋊C4—941no—
1055C22⋊C4—942no—
1056C22⋊C4—942no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—472no—
1061C42—472no—
1062C42—472no—
1063C42—942no—
1064C42—942no—
1065C42—941no—
1066C42—941no—
1067C42—941no—
1068C42D4×D4711yescharacteristic
1069C42D4×D4711yescharacteristic
1070C42C23×D4711yescharacteristic
1071C42C23×D4711yescharacteristic
1072C23—22no—
1073C23—24no—
1074C23—21no—
1075C23—81no—
1076C23—81no—
1077C23—472no—
1078C23—948no—
1079C23—941no—
1080C23—942no—
1081C23—3761no—
1082C23—3761no—
1083C23—3762no—
1084C23—3762no—
1085C23—1882no—
1086C23C2×D4×D4711yescharacteristic
1087Q8—21no—
1088Q8—21no—
1089Q8—472no—
1090Q8—942no—
1091Q8—941no—
1092Q8—3762no—
1093D4—24no—
1094D4—22no—
1095D4—21no—
1096D4—21no—
1097D4—42no—
1098D4—472no—
1099D4—948no—
1100D4—948no—
1101D4—944no—
1102D4—944no—
1103D4—942no—
1104D4—942no—
1105D4—941no—
1106D4—942no—
1107D4—3762no—
1108D4—3762no—
1109D4—3762no—
1110D4—3762no—
1111D4—3762no—
1112D4—1882no—
1113D4C2×#1062535014yes—
1114C2×C4—22no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—41no—
1120C2×C4—42no—
1121C2×C4—44no—
1122C2×C4—42no—
1123C2×C4—81no—
1124C2×C4—82no—
1125C2×C4—81no—
1126C2×C4—472no—
1127C2×C4—472no—
1128C2×C4—472no—
1129C2×C4—948no—
1130C2×C4—941no—
1131C2×C4—944no—
1132C2×C4—944no—
1133C2×C4—942no—
1134C2×C4—942no—
1135C2×C4—941no—
1136C2×C4—941no—
1137C2×C4—942no—
1138C2×C4—3761no—
1139C2×C4—3762no—
1140C2×C4—3762no—
1141C2×C4—3762no—
1142C2×C4—3762no—
1143C2×C4—3762no—
1144C2×C4—3761no—
1145C2×C4—1882no—
1146C2×C4—1882no—
1147C2×C4—1884no—
1148C2×C4C2×D4×D4711yescharacteristic
1149C2×C4C2×D4×D4711yescharacteristic
1150C2×C4C2×D4×D4711yescharacteristic
1151C2×C4C2×D4×D4711yescharacteristic
1152C2×C4C2×D4×D4711yescharacteristic
1153C2×C4#41×D4712yes—
1154C2×C4C2×#1062535012yes—
1155C2×C4C24×D4711yescharacteristic
1156C8—22no—
1157C8—22no—
1158C8—941no—
1159C8—941no—
1160C8—941no—
1161C8—941no—
1162C22—21no—
1163C22—21no—
1164C22—24no—
1165C22—42no—
1166C22—42no—
1167C22—41no—
1168C22—41no—
1169C22—41no—
1170C22—84no—
1171C22—942no—
1172C22—942no—
1173C22—942no—
1174C22—942no—
1175C22—3764no—
1176C22—3768no—
1177C22—1882no—
1178C22—1882no—
1179C22—1882no—
1180C22—1881no—
1181C22—1881no—
1182C22#1568963212yes—
1183C22C22×D4×D4711yescharacteristic
1184C4—21no—
1185C4—21no—
1186C4—21no—
1187C4—42no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—942no—
1192C4—942no—
1193C4—942no—
1194C4—942no—
1195C4—1881no—
1196C4—1882no—
1197C4—1881no—
1198C4#1568963212yes—
1199C4#1568992712yes—
1200C4C2×#41×D4711yescharacteristic
1201C4C22×#1062535011yescharacteristic
1202C2—22no—
1203C2—44no—
1204C2—81no—
1205C2—3762no—
1206C2—1882no—
1207C2—1882no—
1208C2C2×#1568963211yescharacteristic
1209C2C2×#1568992711yescharacteristic
1210C2#2025816111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC4×AGL(1,ℤ/8)×C47C2
socleC22×C47C23×D4
hypercenterC4×AGL(1,ℤ/8)D47
hypocenterC47#60570
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20256804C2semidirect
2. C4×#13094069C2semidirect
3. #20253654C2semidirect
4. #20253630C2semidirect
5. #20253591C2semidirect
6. #20253576C2semidirect
7. #20253444C2semidirect
8. #20253439C2semidirect
9. #20253410C2semidirect
10. #20253386C2semidirect
11. #20253365C2semidirect
12. #20253348C2semidirect
13. #20253238C2semidirect
14. #20253221C2semidirect
15. #20252926C2semidirect
16. #20252893C2semidirect
17. #20252691C2semidirect
18. #20252657C2semidirect
19. C4×#13094052C2semidirect
20. C4×#13094044C2semidirect
21. C2×C4×#10625334C2semidirect
22. #20252033C2semidirect
23. C4×AGL(1,ℤ/8)×C47C2semidirect
28. #15689751C22semidirect
29. #15689745C22semidirect
32. #15689724C22semidirect
36. #15689687C22semidirect
38. #15689670C22semidirect
39. #15689660C22semidirect
45. #15689602C22semidirect
49. #15689595C22semidirect
53. C4×#10625352C22semidirect
54. C2×C4×D188C22semidirect
57. C4×D4×D47C22semidirect
58. #15689462C22semidirect
59. #15689457C22semidirect
60. #15689450C22semidirect
61. #15689449C22semidirect
62. #15689446C22semidirect
63. #15689443C22semidirect
64. #15689438C22semidirect
65. #15689435C22semidirect
66. #15689433C22semidirect
67. #15689425C22semidirect
68. #15689422C22semidirect
69. #15689421C22semidirect
70. #15689417C22semidirect
71. #15689411C22semidirect
72. #15689402C22semidirect
73. #15689401C22semidirect
74. #15689348C22semidirect
75. #15689341C22semidirect
76. #15689340C22semidirect
77. #15689340C22semidirect
78. #15689322C22semidirect
79. #15689317C22semidirect
80. #15689316C22semidirect
81. #15689316C22semidirect
82. #15689282C22semidirect
83. #15689272C22semidirect
86. #15689265C22semidirect
89. #15689255C22semidirect
90. #15689236C22semidirect
91. #15689225C22semidirect
92. C4×#10625337C22semidirect
93. C4×#10625337C22semidirect
94. C4×#10625325C22semidirect
95. C4×#10625336C22semidirect
96. C4×#10625336C22semidirect
97. C4×#10625335C22semidirect
98. C4×#10625335C22semidirect
99. C4×D376C22semidirect
100. C4×#10625334C22semidirect
101. C4×#10625334C22semidirect
102. C4×#10625334C22semidirect
103. C4×#10625334C22semidirect
104. C4×#10625334C22semidirect
105. C4×#10625334C22semidirect
106. #15689185C22semidirect
107. #15689185C22semidirect
108. #15689174C22semidirect
109. #15689174C22semidirect
110. #15689165C22semidirect
111. #15689159C22semidirect
112. C2×#13093957C22semidirect
113. #15689151C22semidirect
114. #15689151C22semidirect
115. #15689129C22semidirect
117. #15689119C22semidirect
120. C2×#13093944C22semidirect
123. C2×C4×C47⋊C8C22semidirect
125. C4×#41×C47C22semidirect
127. C47×#442C22semidirect
128. C47×#440C22semidirect
129. C4×SD16×C47C22semidirect
130. C4×D8×C47C22semidirect
131. C47×#428C22semidirect
133. C47×#417C22semidirect
134. C4×M16×C47C22semidirect
327. C2×D4×C47#41semidirect
362. #10625350#41semidirect
616. C4×AGL(1,ℤ/8)D47semidirect
660. C4×#41C2×D47semidirect
699. #442C2×D47semidirect
701. #440C2×D47semidirect
709. C4×SD16C2×D47semidirect
717. C4×D8C2×D47semidirect
723. #428C2×D47semidirect
731. #417C2×D47semidirect
738. C4×M16C2×D47semidirect
740. C47#60570semidirect
963. C2×D4#10625350semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202568042
C4×#130940692
#202536542
#202536302
#202535912
#202535762
#202534442
#202534392
#202534102
#202533862
#202533652
#202533482
#202532382
#202532212
#202529262
#202528932
#202526912
#202526572
C4×#130940522
C4×#130940442
C2×C4×#106253342
#202520332
C4×AGL(1,ℤ/8)×C472
#6057047